Theresa May is under pressure to bring forward the publication of her own proposals for the Northern Ireland border amid urgent Brexit meetings in Brussels between Irish leaders and Michel Barnier.

Ireland’s premier Leo Varadkar held talks in Brussels on Thursday with European Council president Donald Tusk and chief negotiator Mr Barnier, after which he said he was “very keen” for the issue to be resolved soon.

Mrs May has promised new proposals to the issue and, according to reports, details that have been so far seen by Brussels officials have been tentatively welcomed.

And more positive noises came from the EU suggesting steps towards a compromise – with one source telling Reuters that Mr Barnier was looking at where the bloc could make improvements to what it had offered and was “definitely engaging with Britain”.

Michel Barnier (R) welcomes Irish Prime Minister Leo Varadkar (L) prior to a meeting at the European Commission building in Brussels, on October 4, 2018. (Getty Images)

He tweeted that he had met leaders or deputy leaders from four parties “to discuss the ongoing Brexit negotiations and the importance of a legally operative backstop”.

There has been debate as to whether a variation of a so-called Canada-style trade deal could solve the issue of the border, but former Irish PM Bertie Ahern said that he didn’t believe it was the correct solution to the problem.

Would a Canada-style deal work?

“All you have to do is Google and see what goes on at the Canadian border,” he said on Sky News. “There are huge backlogs of traffic and a huge amount of checks – we want a frictionless open border with no checks.”

Mrs May has so far rejected the EU’s proposal for a “backstop” to ensure there is no return to a hard border between Northern Ireland and the Republic after Brexit, arguing that it would effectively impose a border between the North and the rest of the UK.

But with EU leaders set to meet again later this month in Brussels to review progress in the negotiations, Dublin’s Europe Minister, Helen McEntee said they needed to see Mrs May’s promised alternative as soon as possible.

“I do believe that we can reach an agreement. I am confident given the fact that we have done a huge amount of work on the withdrawal agreement,” she told BBC Radio 4’s Today programme.

October summit is ‘moment of truth’

“I do think there is a lot of common ground in terms of the future relationship moving forward, so we are really now at the critical point.

“I think in the next 10 days if there is a proposal, obviously on its own it won’t resolve the border issue, but certainty if something is legally sound and workable, I do believe that the (EU’s Brexit) taskforce will work with Prime Minister May.”

Michel Barnier greets Theresa May (Photo by Jack Taylor/Getty Images)

“We have 10 days between the teams to negotiate and we have seen what has happened in a short space of time previously. I think where the will is there it can be done, and I do believe the will is there.”

Mr Tusk and Mr Barnier have said the next EU summit on October 18-19 will be the “moment of truth” when it should be become clear whether it is possible for the two sides to reach an agreement.

Meeting with the DUP next week

In Brussels on Thursday, Mr Varadkar welcomed the EU’s “ongoing solidarity” with Ireland.

He said Ireland’s objectives remained as they have been since the start of the process – protecting the Common Travel Area on the island; ensuring no hard border; protecting the rights of Irish citizens living in Northern Ireland; and striking a trade deal with the UK.

“I want to very much agree with Donald Tusk in his call for us to get down to business,” he added. “I am very keen to see an agreement concluded by November if at all possible – that is the interests of Ireland, the EU and the UK.”

Mr Barnier is also due to meet senior figures from the biggest party, the Democratic Unionists, on Tuesday.

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